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# hw02 - CS 154 Intro to Automata and Complexity Theory...

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CS 154 Intro. to Automata and Complexity Theory Handout 6 Autumn 2006 David Dill October 10, 2006 Problem Set 2 Due: October 17, 2006 Homework: (Total 100 points + 20 extra) Do the following exercises. Problem 1. [10 points] Consider the -NFA defined in the following tran- sition table. a b c p { q, r } { q } { r } q { p, q } { p } { p, r } * r a). Compute the -closure of each state. b). Convert this -NFA into an DFA using the construction described in class. You must provide the transition table of the resulting DFA. Problem 2. [20 points] Provide regular expressions for the following lan- guages over the alphabet Σ = { 0 , 1 } . Provide a brief explanation as to why your regular expressions generate the given languages. a). The set of all strings not containing 111 as a substring. b). The set of all strings in which all pairs of adjacent 0’s appears before all pairs of adjacent 1’s. Problem 3. [15 points] Consider the DFA M = ( Q, Σ , δ, q 0 , F ) with Q = { 1 , 2 , 3 , 4 } , Σ = { a, b, c } , q 0 = 1, F = { 4 } , and δ as defined in the following transition diagram.

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